No, to reason thusly is to deny a Judaeo-Chritian world view. In my opinion one ought to be careful citing 'observation and experience' when what one is really citing is the dogma of one's particular religion.
We encounter people with cognitive functions all the way along a continuum, from fully alert and aware, to deeply vegetative. I would say observation is very much consistent with a continuum between life and non-life. In fact, if it were really an either/or thing, decisions whether to continue medical treatment would not be so difficult.
What percentage dead would you consider yourself to be?
But we are not speaking of a continuum of cognitive function. We are speaking of life and death. Whether a thing is dead or alive does not depend on our observation of it. A corpse will rot just as well despite the presence or absence of an observer.
Arguably, there is a continuum of cognitive function that pertains to individuals, as well as to populations (as you suggest). We might say that cognitive function increases from infancy, reaches a peak somewhere on the spectrum, and then begins to decline with age. But this would be a generalization. And to speak of a continuum of cognitive function pertaining to a population is also a generalization.
But the living vs. non-living question is not a question of this type. There is a specific answer, and only one specific answer to the question: Is the organism dead or alive? It seems you are trying to change the subject, RWP.
Re: As to whether I am coming at this problem through a filter of religious dogma: as a dogmatist yourself, how would you really be in a position to know?
The difference between life and non-life is not so difficult to determine, in my opinion.
In terms of the precise moment that a human is dead, and the soul exits the body, that can be a bit vague, and the assumption that there is a soul to leave the body is as you say a religious assumption (though not only judeo-christian).
But at the cellular level, its not so difficult. We tend to think of a cell as a very simple building block, but in fact it is quite a complex mechanism, with quite a complex series of processes and moving parts that are necessary for it to renew itself as well as to fulfill its function in the larger organism. It has a series of events that must occur, and must occur in a certain sequence for it to renew itself. The moment it begins to fail would be fairly clear cut, and the moment it fails completely would not be that difficult to determine, its just a function of having a microscope sufficient to the task.
There would be a series of failures that would precede the final failure, but still the moment of death at the cellular level would be a fairly discrete and observable event.
The loss of a single cell to a complex creature like an animal does not lead to the death of the animal, but the death or failure of enough would lead to a cascading effect leading to the final catastrophic collapse of the whole organism. In purely animal terms, when the last brain cell stops processing, the animal is dead. When, in the case of a human animal, the soul departs and if there might be some physiological marker of that passage is not so easily defined, at least as of yet.
If you're a hospital administrator trying to decide whether or not to continue treatment, life with hope for recovery, and life with no hope for recovery can be a tough call in some of the more difficult cases. But dead is usually pretty clear-cut.